Methods for determining the resistivity of a polycrystalline silicon melt

ABSTRACT

Methods for forming single crystal silicon ingots with improved resistivity control. The methods involve growth and resistivity measurement of a sample rod. The sample rod may have a diameter less than the diameter of the product ingot. The resistivity of the sample rod may be measured directly by contacting a resistivity probe with a planar segment formed on the sample rod. The sample rod may be annealed in a thermal donor kill cycle prior to measuring the resistivity.

FIELD OF THE DISCLOSURE

The field of the disclosure relates to methods for forming singlecrystal silicon ingots with improved resistivity control and, inparticular, methods that involve growth and resistivity measurement of asample rod. In some embodiments, the sample rod has a diameter less thanthe diameter of the product ingot.

BACKGROUND

Single crystal silicon, which is the starting material for mostprocesses for the fabrication of semiconductor electronic components, iscommonly prepared by the so-called Czochralski (CZ) process wherein asingle seed crystal is immersed into molten silicon and then grown byslow extraction. Molten silicon is contaminated with various impurities,among which is mainly oxygen, during the time it is contained in aquartz crucible. Some applications, such as advanced wirelesscommunication applications, insulated gate bipolar transistors (IGBT)and low power, low leakage devices, require wafers with a relativelyhigh resistivity such as 1500 ohm-cm (Ω-cm) or more.

Highly pure polysilicon is used for high resistivity ingot production.Highly pure polysilicon is characterized by a spread in the impurityprofile which causes a wide spread in the intrinsic resistivity range ofthe un-doped material and its type. Targeting of the seed-endresistivity in such high or ultra-high resistivity materials isdifficult due to the variability of boron and phosphorous in thestarting material (including surface boron and phosphorous in thepolysilicon material) and due to impurities in the crucible, and/oroxygen levels which alter the resistivity after a thermal donor killcycle. Further, such high resistivity applications may be susceptible toincreased error in resistivity measurement.

A need exists for methods for preparing high resistivity silicon ingotsthat allow the impurity concentration and/or resistivity of thepolysilicon starting material to be sampled relatively quickly and/orthat allow the resistivity to be measured relatively quickly with arelatively small amount of silicon being consumed for resistivitymeasurement and/or that allow for better resistivity control and/or thatsimplify extrinsic doping processes.

This section is intended to introduce the reader to various aspects ofart that may be related to various aspects of the disclosure, which aredescribed and/or claimed below. This discussion is believed to behelpful in providing the reader with background information tofacilitate a better understanding of the various aspects of the presentdisclosure. Accordingly, it should be understood that these statementsare to be read in this light, and not as admissions of prior art.

SUMMARY

One aspect of the present disclosure is directed to a method forproducing a single crystal silicon ingot from a silicon melt held withina crucible. Polycrystalline silicon is added to the crucible. Thepolycrystalline silicon is heated to cause a silicon melt to form in thecrucible. A sample rod is pulled from the melt. The sample rod has adiameter. The sample rod is annealed to annihilate thermal donors. Aresistivity of the sample rod is measured after annihilation of thermaldonors. A product ingot is pulled from the melt. The product ingot has adiameter. The diameter of the sample rod is less than the diameter ofthe product ingot.

Another aspect of the present disclosure is directed to a method fordetermining the resistivity of a polycrystalline silicon melt heldwithin a crucible. A sample rod is pulled from the melt. The sample rodis annealed in a thermal donor kill cycle. A current is applied to thesample rod. The sample rod is contacted with a resistivity probe whileapplying current to the sample rod to measure the resistivity of therod.

Various refinements exist of the features noted in relation to theabove-mentioned aspects of the present disclosure. Further features mayalso be incorporated in the above-mentioned aspects of the presentdisclosure as well. These refinements and additional features may existindividually or in any combination. For instance, various featuresdiscussed below in relation to any of the illustrated embodiments of thepresent disclosure may be incorporated into any of the above-describedaspects of the present disclosure, alone or in any combination.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic side view of a pulling apparatus for forming asingle crystal silicon ingot;

FIG. 2 is a sample rod grown from a silicon melt;

FIG. 3 is the sample rod with a planar segment formed on its surface;

FIG. 4 is a measurement apparatus for measuring the resistivity of thesample rod;

FIG. 5 is an I-V curve used to measure resistivity of a sample rod; and

FIG. 6 is a scatter plot of the resistivity of a sample rod at variouspositions from the seed end.

Corresponding reference characters indicate corresponding partsthroughout the drawings.

DETAILED DESCRIPTION

Provisions of the present disclosure are directed to methods forproducing a single crystal silicon ingot by the Czochralski method inwhich a sample rod is grown to determine the resistivity of the melt.The sample rod has a diameter less than the product ingot.

In accordance with embodiments of the present disclosure and withreference to FIG. 1, the product ingot is grown by the so-calledCzochralski process in which the ingot is withdrawn from a silicon melt44 held within a crucible 22 of an ingot puller 23. The ingot puller 23includes a housing 26 that defines a crystal growth chamber 16 and apull chamber 20 having a smaller transverse dimension than the growthchamber. The growth chamber 16 has a generally dome shaped upper wall 45transitioning from the growth chamber 16 to the narrowed pull chamber20. The ingot puller 23 includes an inlet port 7 and an outlet port 12which may be used to introduce and remove a process gas to and from thehousing 26 during crystal growth.

The crucible 22 within the ingot puller 23 contains the silicon melt 44from which a silicon ingot is drawn. The silicon melt 44 is obtained bymelting polycrystalline silicon charged to the crucible 22. The crucible22 is mounted on a turntable 31 for rotation of the crucible 22 about acentral longitudinal axis X of the ingot puller 23.

A heating system 39 (e.g., an electrical resistance heater) surroundsthe crucible 22 for melting the silicon charge to produce the melt 44.The heater 39 may also extend below the crucible as shown in U.S. Pat.No. 8,317,919. The heater 39 is controlled by a control system (notshown) so that the temperature of the melt 44 is precisely controlledthroughout the pulling process. Insulation (not shown) surrounding theheater 39 may reduce the amount of heat lost through the housing 26. Theingot puller 23 may also include a heat shield assembly (not shown)above the melt surface for shielding the ingot from the heat of thecrucible 22 to increase the axial temperature gradient at the solid-meltinterface.

A pulling mechanism (not shown) is attached to a pull wire 24 thatextends down from the mechanism. The mechanism is capable of raising andlowering the pull wire 24. The ingot puller 23 may have a pull shaftrather than a wire, depending upon the type of puller. The pull wire 24terminates in a pulling assembly 58 that includes a seed crystal chuck32 which holds a seed crystal 6 used to grow the silicon ingot. Ingrowing the ingot, the pulling mechanism lowers the seed crystal 6 untilit contacts the surface of the silicon melt 44. Once the seed crystal 6begins to melt, the pulling mechanism slowly raises the seed crystal upthrough the growth chamber 16 and pull chamber 20 to grow themonocrystalline ingot. The speed at which the pulling mechanism rotatesthe seed crystal 6 and the speed at which the pulling mechanism raisesthe seed crystal (i.e., the pull rate v) are controlled by the controlsystem.

A process gas is introduced through the inlet port 7 into the housing 26and is withdrawn from the outlet port 12. The process gas creates anatmosphere within the housing 26 and the melt and atmosphere form amelt-gas interface. The outlet port 12 is in fluid communication with anexhaust system (not shown) of the ingot puller.

In this regard, the ingot puller 23 shown in FIG. 1 and described hereinis exemplary and other crystal puller configurations and arrangementsmay be used to pull a single crystal silicon ingot from a melt unlessstated otherwise.

In accordance with embodiments of the present disclosure, afterpolycrystalline silicon is added to the crucible 22 and the heatingsystem 39 is operated to melt-down the polycrystalline silicon, a sampleingot or rod is pulled from the melt. An example sample rod 5 is shownin FIG. 2. The rod 5 includes a crown portion 21 in which the rodtransitions and tapers outward from the seed to reach a target diameter.The rod 5 includes a constant diameter portion 25 or cylindrical mainbody or simply “body”, of the crystal which is grown by increasing thepull rate. The main body 25 of the sample rod 5 has a relativelyconstant diameter. The rod 5 includes a tail or end-cone 29 in which therod tapers in diameter after the main body 25. When the diameter becomessmall enough, the rod is then separated from the melt. The rod 5 has acentral longitudinal axis A that extends through the crown 21 and aterminal end 33 of the ingot.

The growth conditions of the sample rod 5 may be selected from generallyany of the suitable growth conditions available to those of skill in theart. The sample rod 5 may be grown with a locked seed lift (i.e., fixedpull speed with varying diameter such as +/−about 5 mm) or active seedlift (pull speed varied to maintain target diameter).

The sample rod 5 has a diameter less than the product ingot that isgrown after the sample rod. For example, the diameter of the sample rodmay be less than 0.75 times the times the diameter of the product ingot,less than 0.50 times, less than about 0.25 times or less than 0.1 timesthe diameter of the product ingot. In some embodiments, the diameter ofthe sample rod is less than about 150 mm or less than about 100 mm, lessthan about 50 mm, less than about 25 mm, or less than about 20 mm (e.g.,from about 5 mm to about 150 mm, from about 5 mm to about 100 mm, fromabout 5 mm to about 50 mm, from about 5 mm to about 25 mm or from about10 mm to about 25 mm). Generally, the diameter of the rod 5 is measuredby measuring the rod along several axial locations (e.g., within aconstant diameter portion of the rod if the rod has a crown and/ortapered end) and averaging the measured diameters (e.g., measuring 2, 4,6, 10 or more diameters across the length and averaging). In someembodiments, the largest diameter of the sample of the rod is less thanabout 150 mm or less than about 100 mm, less than about 50 mm, less thanabout 25 mm, or less than about 20 mm (e.g., from about 5 mm to about150 mm, from about 5 mm to about 100 mm, from about 5 mm to about 50 mm,from about 5 mm to about 25 mm or from about 10 mm to about 25 mm).

In some embodiments, the rod 5 has a diameter that generally correspondsto the diameter of the neck portion of a product ingot grown in thecrystal puller. For example, the rod may have a diameter of less than 50mm, less than 25 mm, or less than 20 mm.

The sample rod 5 may have any suitable length. In some embodiments, therod (e.g., after cropping) has a length of less than about 300 mm, lessthan about 200 mm or less than about 100 mm (e.g., about 25 mm to about300 mm).

After the sample rod 5 is grown, the resistivity of the sample rod 5 ismeasured. The rod 5 is removed from the ingot puller 23 and is processedto allow the resistivity to be measured. The crown and tail of the ingotmay be removed, such as by use of a wire saw. In some embodiments, thecropped ends of the rod 5 are ground to flatten the ends. The rod endsmay be etched (e.g., mixed acid etched). The rod 5 may be modified toinclude ohmic contacts such as ohmic contacts at its first and secondends 15, 17. For example, the cut ends 15, 17 of the rod 5 may bepainted with a colloidal silver paint and dried.

A planar segment 11 (FIG. 3) is formed on a surface of the rod 5. Theplanar segment 11 may extend axially along the rod 5. In someembodiments, the planar segment 11 extends axially from the first end 15to the second end 17 of the rod 5. In other embodiments, the planarsegment 11 extends only partially along its length.

The planar segment 11 may be formed by grinding a surface of the samplerod 5 such as by use of a grinding pad (e.g., diamond grit pad). In someembodiments, the planar segment has a width sufficient to allow contactwith a voltage probe (e.g., about 2-4 mm). The planar segment 11 may becleaned such as by washing with deionized water and drying beforeresistivity measurement.

In some embodiments, the sample rod 5 is subjected to a rapid thermalanneal before measuring the resistivity. The rapid thermal anneal mayact as a thermal donor kill cycle (i.e., annihilation of thermal donors)by dissociating interstitial oxygen clusters. In some embodiments, theanneal is at a temperature of about 500° C. or more, about 650° C. ormore or about 800° C. or more (e.g., 500° C. to about 1000° C., fromabout 500° C. to about 900° C. or from about 650° C. to about 1100° C.)for at least about 5 seconds, at least about 30 seconds, at least about1 minute or at least about 3 minutes or more (e.g., from about 5 secondsto 15 minutes, from about 5 seconds to about 5 minutes or from about 5seconds to about 3 minutes).

The resistivity of the rod 5 may be measured from the planar segment 11.In some embodiments of the present disclosure, current is driven throughthe rod 5 and a resistivity probe is contacted at one or more locationsalong the length of rod 5. Current may be applied to the rod 5 throughone of the ends 15, 17.

In some embodiments, the rod 5 is secured within a measurement apparatussuch as the apparatus 43 shown in FIG. 4. The measurement apparatus 43includes a clamp 51 that secures the rod 5. The clamp 51 has a firstsupport 53 that secures the rod 5 toward its first end 15 and a secondsupport 55 that secures the rod 5 toward its second end 17. The supports53, 55 are configured to secure the rod between the supports 53, 55(e.g., threaded for adjustment and clamping). The supports 53, 55 maycontact ohmic contacts on the cropped ends of the rod 5. A probe tip 61is caused to contact the rod 5 on the flat planar segment of the rod.Current is passed through the supports 53, 55 and the voltage ismeasured by the probe tip 61. The probe tip 61 is moved manually downthe axis of the rod 5 with current applied/voltage being measured ateach point. In the illustrated apparatus 43, the probe tip 61 is movedmanually. In other embodiments, the probe tip 61 is moved by actuators.

The measurement apparatus 43 of FIG. 4 is an example apparatus and anysuitable apparatus for securing and/or measuring the resistivity of therod may be used unless stated otherwise. Use of a rod (e.g., generally snarrow diameter rod such as less than 100 mm, 50 mm or less than 25 mm)and the measurement apparatus 43 allows the resistivity to be measuredwithout slicing the rod into wafers or slugs.

The resistivity probe may be a two point probe in which both probe tipsare contacted with the planar segment 11. The voltage difference ismeasured across the two probe tips. For example, resistivity may bemeasured with a two-point probe in accordance with SEMI StandardMF397-0812, entitled “Test Method for Resistivity of Silicon Bars usinga Two-Point Probe,” which is incorporated herein by reference for allrelevant and consistent purposes. The 2-terminal or 3-terminalrectification method may be used to determine the crystal type (i.e.,N-type or P-type). Such type determination may be performed inaccordance with SEMI Standard MF42-0316, entitled “Test Method forConductivity Type of Extrinsic Semiconducting Materials”, which isincorporated herein by reference for all relevant and consistentpurposes. Both 2-terminal and 3-terminal rectification methods arerobust methods for very high resistivity silicon.

The voltage may be measured at various points across the length. Themeasured voltages and the sample length and average diameter may be usedto calculate the resistivity such as by determining the slope of acurrent-voltage curve (e.g., Example 1 below).

In some embodiments, the sample rod 5 has a relatively low oxygencontent such as an oxygen content of less than about 5.5 ppma. In otherembodiments, the oxygen content of the sample rod is less than 5.2 ppma,less than 5.0 ppma, less than 3.5 ppma, less than about 3 ppma or evenless than about 2.5 ppma. In some embodiments, the sample rod 5 is freeof dislocations.

The measured resistivity of the rod 5 provides information related tothe resistivity of the polycrystalline silicon melt in the crucible(i.e., the starting dopant impurity concentration (i.e., netdonor-acceptor concentration)). The measured resistivity of the rod 5may be used to adjust the manufacturing conditions for the subsequentlygrown ingot. For example, an amount of dopant may be added to thepolycrystalline silicon melt with the amount of dopant being adjustedbased at least in part on the measured resistivity (e.g., by use of amodel that predicts product ingot resistivity). Suitable dopants includep-type dopants such as boron, aluminum, gallium and indium and n-typedopants such as phosphorous, arsenic and antimony.

In some embodiments, an amount of dopant is added to the melt beforegrowing the sample rod and measuring the resistivity of the rod and anamount of dopant (e.g., the same dopant or a different dopant) is addedafter the sample rod is grown. In other embodiments, all dopants (ifany) are added after the sample rod is grown and the resistivity ismeasured (e.g., boron or phosphorous).

The polysilicon to which the dopant is added and from which a sampleingot and product ingot is pulled may be semiconductor gradepolysilicon. When semiconductor grade polysilicon is used, in someembodiments the polysilicon has a resistivity greater than 4,000 Ω-cmand contains no more than 0.02 ppba boron or phosphorous.

After the sample rod is pulled and, optionally, dopant is added to themelt, a product ingot is withdrawn from the melt. The product ingot hasa diameter greater than the diameter of the sample rod (i.e., thediameter of the constant diameter portion of the sample rod is less thanthe diameter of the constant diameter portion of the ingot). The productingot may have a diameter of about 150 mm or, as in other embodiments,about 200 mm, about 300 mm or more (e.g., 450 mm or more).

In some embodiments, polycrystalline silicon is not added during thegrowth of the ingot (e.g., as in a batch process). In other embodiments,polycrystalline silicon is added to the melt as the product ingot isgrown (e.g., as in a continuous Czochralski method)

The amount of dopant added to the melt (with or without addition of afirst dopant before the sample rod is grown) may be controlled toachieve a target resistivity in at least a portion of the main body ofthe ingot (e.g., a prime portion of the ingot). In some embodiments, thetarget resistivity is a minimum resistivity. In some embodiments, theentire length of the ingot (e.g., length of the body of the ingot) hasthe target resistivity (e.g., minimum resistivity). In some embodiments,the target resistivity of at least a portion of the product ingot is aminimum resistivity of at least about 1,500 Ω-cm or, as in otherembodiments, at least about 2,000 Ω-cm, at least about 4,000 Ω-cm, atleast about 6,000 Ω-cm, at least about 8,000 Ω-cm, at least about 10,000Ω-cm or from about 1,500 Ω-cm to about 50,000 ohm-cm or from about 8,000Ω-cm to about 50,000 Ω-cm. Alternatively or in addition, the sample rodmay have a resistivity of at least about 1,500 Ω-cm, or at least about2,000 Ω-cm, at least about 4,000 Ω-cm, at least about 6,000 Ω-cm, atleast about 8,000 Ω-cm, at least about 10,000 Ω-cm, from about 1,500Ω-cm to about 50,000 ohm-cm or from about 8,000 Ω-cm to about 50,000Ω-cm.

Compared to conventional methods for producing a single crystal siliconingot, the methods of the present disclosure have several advantages.Relatively high purity polysilicon that is used to produce relativelyhigh resistivity single crystal silicon has a wide spread in boron andphosphorous impurity amounts which causes a wide spread in the intrinsicresistivity. By growing a sample rod with relatively small diameter(e.g., less than the product ingot such as less than 100 mm, less than50 mm, less than 25 mm or even less than 10 mm compared to sample ingotsthat have a size substantially the same of the product ingot such as atleast 200 mm), the resistivity of the melt can be sampled relativelyquickly. The measured resistivity may be used for more precise additionof dopant to achieve better targeting of high resistivity or ultra-highresistivity products (e.g., at least about 3000 ohm-cm, 5000 ohm-cm orat least 7000 ohm-cm or more) and, in particular, for better seed-endresistivity targeting. The relatively small diameter sample rod consumesrelatively little amount of the melt (e.g., less than 1 kg, less than0.5 kg or about 0.25 kg or less compared to a full diameter short ingotwhich may consume 15 kg, 20 kg or 50 kg or more of the melt) and reducesimpurity build-up attributed to the sampling process. The sample rod maybe grown relatively quickly (e.g., about 12, 10 or even 5 hours or lesscompared to a full size short ingot which may involve 20 hours, 30hours, 40 hours, or 50 hours of growth time). The sample rod may have arelatively low oxygen content (e.g., such as less than about 5 ppma orless than 4 ppma) which may improve the accuracy of the resistivitymeasurement (e.g., the accuracy of the rod after a thermal donor killcycle).

In embodiments in which a planar segment is formed on the surface of thesample rod, the resistivity may be measured by a two-point probe. Suchtwo-point probes may reduce sample preparation, may be less sensitive togeometric correction factors and may allow for better current contactsrelative to four-point probes. Use of a two-point probe also allows useof a 2-terminal or 3-terminal rectification method fortype-determination of the ingot.

Reduced sample rod growth time and reduced resistivity measurement timesreduce the processing time at which the resistivity measurement isprovided (e.g., 20, 30 or 40 hours in reduction of process time) whichreduces impurity buildup caused by crucible dissolution. Reducingimpurities also improves resistivity predictability for future runs.Reduction in the hot hour time for each batch (i.e., between productingots) allows for the crucible to recharged in additional cycleswithout an increase in loss of zero dislocation.

EXAMPLES

The processes of the present disclosure are further illustrated by thefollowing Examples. These Examples should not be viewed in a limitingsense.

Example 1: Determination of Resistivity from I-V Curve

Voltage of a sample rod was measured axially (e.g., such as with theapparatus of FIG. 4) with the applied current and measured voltage beingrecorded. FIG. 5 shows the I-V curve that was generated. Using thegeometry of the sample and the slope of the I-V curve, the resistivitywas determined to be 6139 ohm-cm for the sample.

Example 2: Comparison of Short Ingot vs Sample Rod

A single crystal short sample ingot (“Short Ingot”) having a diameter ofabout the size of the product rod (e.g., about 200 mm in a 200 mmpulling apparatus) was grown in a pulling apparatus similar to FIG. 1.The crystal was cropped and subjected to a mixed acid etch (MAE). Thecrystal slug was rapid thermal annealed at 800° C. for 3 minutes andlapped. The slug was contacted with a four-point probe to measure theresistivity with the resistivity being averaged over three measurements.

A sample rod (“Sample Rod”) was grown in locked seed lift mode in thesame pulling apparatus after the short ingot was grown. The diameter ofthe rod varied across its length and was within a range of 17-23 mm withan average of 20 mm. The sample rod was cropped and ground to form aflat segment that extended from one end to the other end of the rod. Therod was rapid thermal annealed at 800° C. for 3 minutes. The resistivityof the ingot was measured by a measurement apparatus similar to theapparatus shown in FIG. 4 and with a two-point probe. The differencesbetween the growth conditions are shown in Table 1 below:

TABLE 1 Growth Conditions for Sample Ingot 200 mm in Diameter and aSample Rod ~17-23 mm in Diameter Short Ingot Sample Rod Diameter (mm)207 ~17-23 Weight (kg) 31 0.11 Length (mm) 250 200 Process Time (hr) 255 Resistivity Sample 26 6 Preparation Time (hr) Total time (hr) 51 11

The measured resistivities across the length of the sample rod and theresistivity of a slug from the sample ingot are shown in FIG. 6.

The sample preparation time for the short ingot was 26 hours andinvolved cropping, mixed-acid etch, rapid thermal anneal, slab cutting,grinding (e.g., with a diamond pad), lapping and measurement with a4-point probe. The sample preparation time for the sample rod was 6hours and involved cropping, mixed-acid etch, rapid thermal anneal, flatgrinding (with a diamond pad), lapping and measurement with a 2-pointprobe.

As used herein, the terms “about,” “substantially,” “essentially” and“approximately” when used in conjunction with ranges of dimensions,concentrations, temperatures or other physical or chemical properties orcharacteristics is meant to cover variations that may exist in the upperand/or lower limits of the ranges of the properties or characteristics,including, for example, variations resulting from rounding, measurementmethodology or other statistical variation.

When introducing elements of the present disclosure or the embodiment(s)thereof, the articles “a”, “an”, “the” and “said” are intended to meanthat there are one or more of the elements. The terms “comprising,”“including,” “containing” and “having” are intended to be inclusive andmean that there may be additional elements other than the listedelements. The use of terms indicating a particular orientation (e.g.,“top”, “bottom”, “side”, etc.) is for convenience of description anddoes not require any particular orientation of the item described.

As various changes could be made in the above constructions and methodswithout departing from the scope of the disclosure, it is intended thatall matter contained in the above description and shown in theaccompanying drawing[s] shall be interpreted as illustrative and not ina limiting sense.

What is claimed is:
 1. A method for determining the resistivity of apolycrystalline silicon melt held within a crucible, the methodcomprising: pulling a sample rod from the melt; annealing the sample rodin a thermal donor kill cycle; applying a current to the sample rod; andcontacting the sample rod with a resistivity probe while applyingcurrent to the sample rod to measure the resistivity of the rod.
 2. Themethod as set forth in claim 1 further comprising forming a planarsegment on a surface of the sample rod, the resistivity probe contactingthe planar segment to measure the resistivity of the rod.
 3. The methodas set forth in claim 1 wherein the probe is a two-point resistivityprobe.
 4. The method as set forth in claim 1 wherein the sample rod hasan average diameter, the average diameter of the sample rod being lessthan about 150 mm.
 5. The method as set forth in claim 1 wherein thesample rod has an average diameter, the average diameter of the samplerod being less than about 100 mm.
 6. The method as set forth in claim 1wherein the sample rod has an average diameter, the average diameter ofthe sample rod being less than about 50 mm.
 7. The method as set forthin claim 1 wherein the sample rod has an average diameter, the averagediameter of the sample rod being less than about 25 mm.
 8. The method asset forth in claim 1 wherein the sample rod has a largest diameter, thelargest diameter of the sample rod being less than about 150 mm.
 9. Themethod as set forth in claim 1 wherein the sample rod has a largestdiameter, the largest diameter of the sample rod being less than about50 mm.
 10. The method as set forth in claim 1 wherein the sample rod issecured by a measurement apparatus comprising a clamp that holds thesample rod when contacting the rod with a resistivity probe.
 11. Themethod as set forth in claim 1 wherein the sample rod is annealed priorto measuring the resistivity of the sample rod.
 12. The method as setforth in claim 1 further wherein the sample rod is annealed at atemperature of at least about 500° C.
 13. The method as set forth inclaim 12 wherein a length of the anneal is at least about 5 seconds. 14.The method as set forth in claim 12 wherein a length of the anneal isfrom about 5 seconds to about 5 minutes.
 15. The method as set forth inclaim 1 further wherein the sample rod is annealed at a temperature ofat least about 650° C.
 16. The method as set forth in claim 1 whereinthe sample rod has a length of less than about 300 mm.
 17. The method asset forth in claim 1 wherein the sample rod has a resistivity of atleast about 1,500 Ω-cm.
 18. The method as set forth in claim 1 whereinthe sample rod has a resistivity of at least about 6,000 Ω-cm.
 19. Themethod as set forth in claim 1 wherein the sample rod has a resistivityof at least about 10,000 Ω-cm.